1. Field of the Invention
The present invention relates to a system, apparatus and methodology for digital signal processing, and in particular to finite sampling digital signal processing utilizing Fourier series.
2. Discussion of the Related Art
Digital signal processing (DSP) has permeated into every aspect of modern society. It is utilized in everything from devices that help to create the world-wide web to EKG machines found in hospitals. Generally, any device that requires a signal to be processed by a computer employs digital signal processing. The development of DSP technologies has allowed microprocessors and computers to come of age. DSP is the bridge between the real world “analog” or continuous signals and the microprocessor and computer's required discrete or “digital” domain. For this reason, advancements in DSP technology have afforded breakthroughs in many other areas dependent on information gathered through signal characteristics. These include progressions in the health industries, sciences, engineering and even weather prediction.
This art of taking a continuous or analog signal and creating a representative signal in a digital domain has its beginnings several centuries ago. That statement is normally surprising to most people since the introduction of computers and microprocessors are relatively new compared to the time when Gauss and Newton were providing history with their groundbreaking theories. So, despite being based on centuries-old fundamentals, DSP technologies have mainly progressed in more recent times. The methods of transposing the continuous signals into the digital domain have varied greatly during that time. In order to preserve the fidelity of the original continuous signals, great pains were taken to reproduce every nuance in the digital realm. This led to extremely complex equations which took a tremendous amount of time to process. Thus, the processing “delay” prevented DSP technologies from being utilized “real-time.”
Since DSP, at times, was not fast enough to process continuous signals in real-time, great emphasis was placed on reducing the delay caused by the processing. Advancements in this area of DSP technologies proved to be very beneficial to a multitude of industries and sciences. More information could be gathered, processed, analyzed and used to control or solve many problems as they occurred as close to real-time as possible. This led to an even greater emphasis on speeding up the processing and maintaining accuracy of the conversion of continuous to digital signals. More advancements in the speeds of microprocessors and computers allowed for faster processing even without advancements in the DSP methodologies. Although, these types of progressions will always facilitate the DSP technologies, they will not be able to replace nor match advancements in the art of DSP itself.
The advancement of DSP technologies could be construed to hold the key to advancing a multitude of extremely diverse areas of human intelligence, possibly even being considered a cornerstone in mankind's development. This holds true due to the continued dependence of our sciences on computer and microprocessor technologies in every facet of our lives. Its importance cannot be underestimated in the development of our modern societies. Even a minute incremental advancement is paramount when one understands the thousands of areas that will benefit from that one tiny step forward.
Today, DSP technologies are greatly focused on being faster, more accurate and easier to implement than ever before. We are also challenged by the current rate of microprocessor and computer technological advancements. Every day it seems that they increase their speed two-fold. Older devices become obsolete in a matter of months instead of the previous years. This leaves devices that were implemented at great expense useless to utilize methodologies that are being developed for faster and faster processors. Many industries and sciences cannot afford to constantly upgrade equipment to keep up with the ever exponentially changing processor technology. They are left trying to implement DSP technology designed for a 3 Gigahertz processor in a 100 Megahertz processing device, overwhelmed by the increasing DSP latencies.